The goal of this study is a better understanding of the numerous sound propagation mechanisms in granular materials. In a static, regular (crystal), 3D packing, a small perturbation is created on one side and examined during its propagation through frictionless and frictional packings. The perturbation can be applied in longitudinal and shear direction in order to excite different modes of information propagation, including rotational modes as well. Wave speed and dispersion relation derived from simulation data are compared to those given by a theoretical approach based on a micro-macro transition. The detailed analysis of the wave velocity reveals an interesting acceleration close to the source. Finally a step towards real packings is made by introducing either friction or a tiny (but decisive) polydispersity in the particle size.
Dynamic simulations of wave propagation are performed in dense granular media with a narrow polydisperse size-distribution and a linear contact-force law. A small perturbation is created on one side of a static packing and its propagation, for both P-and S-waves, is examined. A size variation comparable to the typical contact deformation already changes sound propagation considerably. The transmission spectrum becomes discontinuous, i.e., a lower frequency band is transmitted well, while higher frequencies are not, possibly due to attenuation and scattering.This behaviour is qualitatively reproduced for (i) Hertz non-linear contacts, for (ii) frictional contacts, (iii) for a range of smaller amplitudes, or (iv) for larger systems. This proves that the observed wave propagation and dispersion behaviour is intrinsic and not just an artifact of (i) a linear model, (ii) a frictionless packing, (iii) a large amplitude non-linear wave, or (iv) a finite size effect.
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